Question

Gail works in a flower shop, where she produces 10 floral arrangements per hour. She is paid $10 per hour for the first eight hours she works and $15 an hour for each additional hour she works. What is the firm’s cost function? What are its AC, AVC, and MC functions? Draw the AC, AVC, and MC curves.

Answer 1

Cost function $C(x)$

$C(x):Total\ Cost= FC+VC$

$FC=\$10\times 8=\$80$

$VC=\%15 \times h=\$15h$

$\therefore C(x)= 80+15h$

Average Cost

$AC=\frac{TC}{h}$

Q here is equivalent to 10 floral arrangements produced within an hour.

$\therefore AC=(80+15h)/h$

$AC=(\frac{80}{h}+15)$

Average Variable Cost

$AVC= \frac{VC}{h} = \frac{15h}{h}=15$

Marginal Cost

to get the MC, we find the partial derivative of the Total cost thereby maintaining 80 as a constant.

$MC= \frac{\delta TC}{\delta h}=80+15=95$

Graphing the functions we have;